more than one vertex group for one bone
You can not assign more than one Vertex Group to one Bone. However you can assign many vertices to a vertex group where each vertex may have different weight. And that should be exactly the solution for which you are searching.

There is no benefit from splitting the weights for one single bone into different vertex groups. Even if that would be possible, blender had to merge the groups anyways before it could apply the weights to the vertices.

Please also check the wiki documentation about vertex groups:

https://docs.blender.org/manual/en/dev/modeling/meshes/properties/vertex_groups/index.html

You should read all 4 chapters of that section.